Concrete screed with angularly positionable rake guide

ABSTRACT

A floating screed device includes: an elongated float, rigid and spaced-apart rods with the tops thereof defining a planar region having a planar bottom for floating on plastic concrete, a device coupled to the float to determine elevation thereof relative to a target elevation in the plastic concrete, and a support and adjustment (S/A) mechanism that moves the rods based on the elevation so-determined as the floating screed device is moved through a volume of the plastic concrete that is unfinished. In general, the rods are moved by the S/A mechanism such that the planar region defined by the rods rotates about an axis that is parallel to the rods and perpendicular to the longitudinal axis of the float.

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This patent application is co-pending with one related patent application entitled “CONCRETE SCREED WITH PIVOTING LEADING-EDGE BLADE FOR ANGULAR POSITIONING THEREOF”, Ser. No. 12/322,149, filed Jan. 29, 2009, by the same inventors and owned by the same assignee as this patent application.

FIELD OF THE INVENTION

The invention relates generally to screeding devices, and more particularly to a screed device having a leading edge rake guide that can pivot to an angular position with respect to a trailing float.

BACKGROUND OF THE INVENTION

Floating screeds are used to strike off concrete floors or other horizontal surfaces to their desired finished elevation. Conventional floating screeds have a heavy planar float with an elongated edge defining a blade. The blade forms the leading edge of the screed that cuts through a volume of plastic concrete as the screed is pulled therethrough. Excess concrete that builds up on the blade side of the screed is raked away by workers standing in the un-struck concrete. As the float moves over an area of the concrete cut by the blade, the float serves to smooth the concrete thereby leaving a struck-off region of concrete.

Owing to the weight and density of unhardened (wet) concrete, it is necessary for the rake workers to prevent any substantial build up of wet concrete just ahead of the screed as the weight of such excess build up makes the screed operator's job extremely difficult. At the same time, the rake worker attempts to maintain small amounts of excess wet concrete forward of the screed's blade so that there is enough concrete in place to achieve the desired elevation as the screed moves thereover. However, in trying to provide just enough excess concrete, the rake worker often gouges the un-struck concrete to a level that is below the desired finished height of the concrete. This requires the screed operator to wait for the rake worker to push a volume of concrete back into the gouged region.

The un-struck concrete is typically adjacent to a section of already-struck concrete that has not yet hardened. The floor workers generally place a portion of the floating screed on the already-struck concrete thereby referencing one end of the screed to the desired finished elevation/grade plane. To make elevation corrections in the un-struck concrete, the floating screed is essentially lifted up/pushed down on the portion thereof that is in the un-struck concrete. While the goal is to place the screed at the same elevation as the adjacent already-struck concrete, this action tends to tilt the floating screed with respect to the desired finished elevation. Further, since the adjacent already-struck concrete is generally not yet hardened, this tilting action also can cause the floating screed to dig into the adjacent already-struck concrete and/or damage the edge of the adjacent already-struck concrete where it interfaces with the un-struck concrete thereby necessitating repair work.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide a screed device that improves the process of producing smooth and level concrete surfaces at a desired elevation.

Another object of the present invention is to provide an apparatus that makes a concrete rake worker more efficient.

Still another object of the present invention is to provide a floating screed device that can take advantage of a reference elevation defined by adjacent already-struck-but-unhardened concrete without subjecting same to subsequent repair.

Other objects and advantages of the present invention will become more obvious hereinafter in the specification and drawings.

In accordance with the present invention, a floating screed device includes an elongated float having a planar bottom for floating on plastic concrete. A device coupled to the float determines elevation thereof relative to a target elevation in the plastic concrete. The floating screed device also includes a plurality of rigid and spaced-apart rods with the tops thereof defining a planar region. A support and adjustment (S/A) mechanism is coupled to the float, the rods, and the device that determines elevation. The S/A mechanism moves the rods based on the elevation so-determined as the floating screed device is moved through a volume of plastic concrete that is as yet un-struck. The rods form the initial contact between the floating screed device and the volume of the plastic concrete that is to be struck to the desired finished elevation. The rods are moved by the S/A mechanism such that the planar region defined by the rods rotates about an axis that is parallel to the rods and perpendicular to the longitudinal axis of the float.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention will become apparent upon reference to the following description of the preferred embodiments and to the drawings, wherein corresponding reference characters indicate corresponding parts throughout the several views of the drawings and wherein:

FIG. 1 is a schematic perspective view of a floating screed device in accordance with the present invention;

FIG. 2 is a head-on view of an embodiment of the floating screed device illustrating just the float and the spaced-apart rods coupled thereto;

FIG. 3 is a plan view taken along line 3-3 in FIG. 2;

FIG. 4 is an end view taken along line 4-4 in FIG. 2;

FIG. 5 is a head-on view of the embodiment illustrated in FIG. 2 after the rods have been moved such that the plane defined by the rods is inclined with respect to the bottom of the float;

FIG. 6 is a cut-away perspective view of one end of the embodiment illustrated in FIG. 2 depicting an embodiment of a mechanical linkage system used to move the rods;

FIG. 7 is an isolated perspective view of a control arm and rod in accordance with an embodiment of the present invention;

FIG. 8A is a perspective view of the floating screed device operating at a target elevation;

FIG. 8B is a perspective view of the floating screed device with the float thereof tilted below a target elevation; and

FIG. 8C is a perspective view of the floating screed device with the float thereof tilted above a target elevation.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings and more particularly to FIG. 1, a floating screed device in accordance with the present invention is schematically illustrated and is referenced generally by numeral 10. Floating screed device 10 is an elongate device as would be well understood in the art. Floating screed device 10 includes:

(i) an elongate float 12,

(ii) a number of rods 14 spaced apart from one another and distributed along the majority of the length of float 12,

(iii) a support and adjustment (“S/A”) mechanism 16 coupled to each of float 12 and rods 14 where, in general, S/A mechanism 16 maintains the spaced-apart relationship between rods 14 and adjusts the vertical height of each of rods 14 such that the tops of rods 14 always define a plane referenced by dashed lines 18; and

(iv) an elevation determination system 20 coupled to float 12 for determining the elevation of float 12 and for providing such elevation to S/A mechanism 16 to thereby control the vertical heights of rods 14 and position of plane 18.

The functional relationships of the elements and the operation of floating screed device 10 will be explained in greater detail below.

Float 12 is an elongate structure such that its longest dimension has a longitudinal axis 12X associated therewith. Float 12 defines a planar bottom 12A that “floats” on a plastic concrete surface (not shown) to be struck off to a desired finished elevation. In the illustrated embodiment, float 12 is substantially rectangular in cross-sections thereof taken along longitudinal axis 12X and has a beveled, lower leading edge 12B to facilitate movement over concrete.

However, float 12 can be defined by other geometric shapes without departing from the scope of the present invention. Float 12 can be hollow, partially solid, or partially filled with a granular material, a solid material, or a fluid, etc., without departing from the scope of the present invention.

Each of rods 14 is an elongate piece of stiff material coupled to and movable by S/A mechanism 16. More specifically, each of rods 14 has a longitudinal axis 14A that is always parallel to planar bottom 12A with rods 14 always being parallel to one another. S/A mechanism 16 moves rods 14 in a manner that allows plane 18 to be rotated about an axis 17 as indicated by two-headed curved arrow 22. Axis 17 can coincide with the longitudinal axis of the one of rods 14 closest to an end portion 12C of float 12 that extends past the arrangement of rods 14. Axis 17 can also be a virtual axis of plane 18 (as shown) that is parallel to rods 14 and aligned with a part of end portion 12C that is inboard of a longitudinal end of float 12. In either case, axis 17 is also perpendicular to longitudinal axis 12X of float 12. Axis 17 can be coincident with or be parallel to planar bottom 12A without departing from the scope of the present invention. Movement of rods 14 such that plane 18 rotates about axis 17 angularly positions plane 18 with respect to bottom 12A as will be explained further below. Rods 14 will form the initial contact with un-struck concrete as floating screed device 10 is moved through un-struck concrete in a direction that is perpendicular to longitudinal axis 12X of float 12. In other words, rods 14 define the leading edge of floating screed device 10 as it moves through un-struck concrete in the direction of arrow 24.

With respect to rods 14, their shape and construction details can be any that would allow rods 14 to cut through plastic concrete while the tops thereof define plane 18. For example, rods 14 could be rigid pieces of solid or hollow material (e.g., metal, composite, etc.), and can have a circular cross-section as shown. However, it is to be understood that the cross-sectional shape of rods 14 is not a limitation of the present invention.

Rods 14 essentially replace the concrete-cutting blade of a conventional floating screed device while improving the concrete strike off operation. Owing to the weight and density of fresh (wet) concrete, it is necessary for the rake workers (i.e., those workers standing in the un-struck concrete forward of the screed operator) to prevent any substantial build up of wet concrete just ahead of the screed as this makes the screed operator's job extremely difficult.

To prevent a rake worker's removal of too much or too little wet concrete, rods 14 also serve as a novel type of rake guide to provide the rake workers with a guide that would prevent concrete build up at the screed's leading edge.

Spacing between adjacent ones of rods 14 is such that a rake worker's blade (not shown) will rest on at least two of rods 14 when the rake blade is placed thereon. The protruding length of rods 14 defines the width of plane 18 that will be free of concrete build-up as a rake worker pulls wet concrete therealong. The length of rods 14 can be any reasonable length over which they remain rigid. Typically, the length of each rod 14 will be the same, although this is not a requirement of the present invention. Regardless of their shape, any minor grooves formed by rods 14 in the wet concrete are quickly “floated” to the desired finished concrete height as float 12 (tracking behind rods 14) moves thereover.

Rods 14 could also be colored along the length thereof in one or more colors that are different from the color of the plastic concrete being struck off. Rods 14 could be so-colored all along their length or just near their outboard ends. By coloring rods 14 in this way, the rake worker is provided with both tactile feedback (i.e., as the rake contacts rods 14) and visual feedback.

S/A mechanism 16 is any device or combination of elements that couples rods 14 to float 12 in a relationship that supports the rotational movement of plane 18 indicated by arrow 22. In practice, the amount of rotational movement of plane 18 is relatively small (e.g., typically on the order of about 1 degree or less) as screed device 10 moves through wet concrete during a strike-off operation. S/A mechanism 16 would typically include a powered actuator (e.g., hydraulic, electric solenoid, etc.) that could be controlled/operated manually. However, in most applications, screed device 10 includes a height/level defining system (e.g., elevation determination system 20) coupled to S/A mechanism 16 to effect automatic height adjustment of rods 14 to thereby change the angle of inclination of plane 18 as screed device 10 moves through/over un-struck wet concrete.

In accordance with the present invention, elevation determination system 20 is mounted to float 12 such that its elevation measurement location is located near the end of screed device 10 where plane 18 experiences its greatest amount of movement, i.e., near the end of float 12 and approximately aligned with the one of rods 14 that can experience the greatest amount of height adjustment. System 20 can be part of a laser level system, the use of which in concrete floor construction is well known and understood. In general, elevation determination system 20 determines the height of float 12 (e.g., planar bottom 12A of float 12 near the end thereof where plane 18 experiences its greatest amount of movement) relative to a target height that is typically indicative of the desired finished elevation of the concrete.

It has been found that wet concrete tends to bubble up after the leading edge of a screed device passes over/through wet concrete. That is, the leading edge (i.e., rods 14) of a two-section screed device does not necessarily define the desired finished elevation of wet concrete. Accordingly, the present invention uses float 12 to set the ultimate finished elevation of the wet concrete as rods 14 are adjusted in height based on the elevation of float 12 relative to a datum or target elevation. By constructing the floating screed in this way, float 12 corrects the “bubbling concrete” condition to thereby strike off the wet concrete to the desired elevation.

The output of system 20 is an amount of movement of rods 14 (i.e., relative to planar bottom 12A) required to achieve the target height as floating screed device 10 is moved through/over the un-struck concrete. The output of system 20 is supplied to S/A mechanism 16 which, in turn, applies the requisite amount of up or down force to rods 14 to thereby angularly position the defined plane 18 relative to planar bottom 12A.

The above-described angular positioning of plane 18 is necessitated by the general nature of concrete placement and strike-off operations where a region of wet un-struck concrete is generally adjacent to a region of concrete that has already been struck off to its desired finished elevation. Accordingly, one end of screed device 10 (i.e., the longitudinal end opposite the end where elevation determination system 20 is mounted) is generally located on or next to the adjacent already-struck concrete while the remainder of screed device 10 resides on the wet un-struck concrete. To accommodate this scenario, one end of the arrangement of rods 14 is positioned inboard of one end of float 12, e.g., inboard of the left end of float 12 in the illustrated embodiment. As a result, an end portion 12C of float 12 is defined that essentially has no leading edge defined by rods 14. As will be explained later herein, a screed operator will typically place end portion 12C directly on concrete that has already teen struck off to its finished elevation but has not yet hardened. The present invention's ability to angularly position plane 18 relative to float bottom 12A during the screeding process allows the screed device to direct float bottom 12A to the desired finished (i.e. target) elevation as will be explained later herein.

The height adjustment of rods 14 in a way that creates rotational movement of plane 18 can be achieved by a variety of realizations of S/A mechanism 16. Typically, S/A mechanism 16 will include a mechanical system coupled to rods 14 and manual or mechanized means to control/actuate the mechanical system. By way of non-limiting examples, embodiments of suitable mechanical systems will be described herein with reference to FIGS. 2-7. Suitable manual or mechanized actuators for driving these mechanical systems are straightforward and would be readily understood by one of ordinary skill in the art. For clarity of illustration, only float 12, rods 14, and the mechanical aspects of S/A mechanism 16, are illustrated in FIGS. 2-7.

Referring first to FIGS. 2-4, rods 14 are illustrated in their neutral position that is defined when all of the tops of the rods are aligned with the planar bottom 12A of float 12 such that the plane 18 is aligned with planar bottom 12A. Each of rods 14 is coupled to (or made integral with) a control arm 30 formed by a lever 32, an extension 34, and an offset 36. Typically, control arm 30 is constructed as an integral, rigid element. In general, lever 32 is coupled to an actuator (not shown) within float 12. Extension 34 supports lever 32 and offset 36, and is mounted in float 12 for rotation about its longitudinal axis 34A. Offset 36 couples extension 34 to a corresponding rod 14 at a radial distance from axis 34A.

When the heights of rods 14 are to be adjusted to change the angle of inclination of plane 18, levers 32 are pushed/pulled along the length of float 12 to thereby rotate extensions 34 about their respective axes 34A. As a result, rods 14 are moved through circular arcs to incline plane 18 up or down (e.g., up by an angle of inclination α as shown in FIG. 5) relative to the neutral position alignment with planar bottom 12A. To create such rotation of plane 18, each of rods 14 will be adjusted in height by a unique amount. In the illustrated embodiment, the amount of height adjustment gradually increases from left to right as plane 18 rotates about axis 17. As explained earlier herein, axis 17 can be coincident with or in proximity to the one of rods 14 that is closest to end portion 12C.

The relationship of control arms 30 to float 12 and an actuator 40 is best seen in FIG. 6 where the left end of float 12 has been cut away to illustrate two control arm 30/rod 14 combinations. The push/pull force acting on actuator 40 is illustrated by two-headed arrow 42. As mentioned above, the creation of push/pull force 42 can be manually-generated or machine-generated without departing from the scope of the present invention. The simultaneous application of force 42 to each control arm 30 causes the corresponding circular arc movement of each of rods 14 as indicated by dashed arc lines 26.

Since each of rods 14 must be uniquely adjusted in height under the application of force 42, each control arm 30 must be configured to provide the right amount of height adjustment for its corresponding rod 14 in order to maintain the integrity of plane 18 regardless of its angular inclination. With the illustrated embodiment of control arm 30, this can be accomplished in a couple of ways as will now be described with reference to the isolated control arm 30 shown in FIG. 7. In one approach, the place where actuator 40 couples to lever 32 defines how much rotation extension 34 will experience for a given amount of push/pull force 42. Specifically, the greater the radial distance between axis 34A and the point where actuator 40 is coupled to lever 32, the greater amount of rotation of extension 34. If each control arm 30 defines a unique attachment point on its lever 32 for actuator 40, then each rod 14 will be swept through a unique angle as it moves in its circular arc. In another approach, actuator 40 can attach to the same point on each lever 32 such that each extension 34 rotates the same amount for a given push/pull force 42. The different height adjustments are achieved by providing unique lengths for offsets 36. In this way, even though all extensions 34 rotate through the same angle, the circular arcs swept by each rod 14 will be defined by a unique angle.

The present invention improves concrete strike-off accuracy as the floating screed device is more easily manipulated to a desired finished-concrete target elevation.

To illustrate operation of the present invention, reference will now be made to FIGS. 8A-8C where a region 100 of already-struck concrete at a desired target elevation is adjacent to a region 102 of un-struck concrete. For clarity of illustration, rods 14 and S/A mechanism 16 are only depicted in a schematic fashion similar to FIG. 1. Recognizing that screed operators prefer to use an edge of an already-struck region of concrete as a “one side” reference, the present invention is positioned such that the portion 12C of float 12 that extends longitudinally past the arrangement of rods 14 is placed on the finished concrete. Since there is no portion of rods 14 riding on the already-struck concrete, float portion 12C simply “floats” on the already-struck concrete. The advantage is that rods 14 do not come into contact with the already-struck concrete where such contact could result in damage to the already-struck surface.

For purpose of illustration, operations will be described as floating screed device 10 moves in a direction 24 through region 102. Relative to direction 24, the un-struck volume of plastic concrete in region 102 is forward of device 10 while already-struck concrete (not shown) trails device 10. The un-struck volume of plastic concrete in region 102 is typically at a height above the target elevation defined by the surface of region 100 so that rods 14 must cut therethrough.

In use, whatever the orientation of planar bottom 12A of float 12 (e.g., horizontal and at the target elevation, tilted above/below the target elevation), the operational goal of screed device is to direct planar bottom 12A to ride along the desired finished plane of the concrete surface. In FIG. 8A, floating screed device 10 is “on grade” with both rods 14 and planar bottom 12A of float 12 within the target plane defined by the surface of region 100.

In FIG. 8B, bottom 12A of float 12 is tilted below the target plane defined by the surface of region 100. The measured elevation (provided by elevation determination system 20) of the lower end of float 12 is used by S/A mechanism 16 to move rods 14 up by an amount that causes plane 18 to be positioned within the target plane defined by the surface of region 100. As device 10 advances in direction 24, the lower end of float 12 will pitch or “ski” up as it encounters an uphill slope in the concrete created by the rake workers cutting down or filling in the wet concrete to the tops of the raised rods 14.

In FIG. 8C, bottom 12A of float 12 is tilted above the target plane defined by the surface of region 100. This time, S/A mechanism 16 (as controlled by the measurements from elevation determination system 20) moves rods 14 down to position plane 18 at the target plane defined by the surface of region 100. As device 10 advances in direction 24, the higher end of float 12 will pitch or “ski” down as it encounters a downhill slope in the concrete created by the rake workers cutting down or filling in the wet concrete to the tops of the lowered rods 14.

The advantages of the present invention are numerous. The floating screed's leading edge rake guide will be lighter in weight than a conventional screed blade thereby making the present invention easier to maneuver. The “tilting plane” rake guide presents a novel way for a screed operator to take advantage of an already-struck region of concrete adjacent to an un-struck region of concrete. By using the trailing float as the means for gauging the struck surface with respect to a target plane, the present invention corrects the “bubbling concrete” condition that occurs when a screed device has a leading section followed by a second section spaced apart from the leading section.

Although the invention has been described relative to specific embodiments thereof, there are numerous variations and modifications that will be readily apparent to those skilled in the art in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the invention may be practiced other than as specifically described. 

1. A floating screed device comprising: an elongated float having a planar bottom for floating on plastic concrete, said float having a longitudinal axis; a device coupled to said float for determining elevation thereof relative to a target elevation in the plastic concrete; a plurality of rigid and spaced-apart parallel rods with tops of said rods defining a planar region; and a support and adjustment (S/A) mechanism coupled to said float, said rods and said device for determining elevation, said S/A mechanism uniquely adjusting a height of each of said rods relative to said planar bottom of said float based on said elevation so-determined as said floating screed device is moved through a volume of the plastic concrete that is unfinished with said rods defining a leading edge between said floating screed device and the volume of the plastic concrete that is unfinished, wherein said planar region rotates about an axis that is parallel to said rods and perpendicular to said longitudinal axis of said float.
 2. A floating screed device as in claim 1 wherein said S/A mechanism moves each of said rods along a circular arc with each of said rods being swept through a unique angle.
 3. A floating screed device as in claim 1 wherein said S/A mechanism moves each of said rods along a circular arc with each of said rode being swept through the same angle.
 4. A floating screed device as in claim 1 wherein the length of each of said rods is the same.
 5. A floating screed device as in claim 1 wherein the color of each of said rods is different from that of concrete.
 6. A floating screed device as in claim 1 wherein said axis is one of coincident with said planar bottom and parallel to said planar bottom.
 7. A floating screed device as in claim 1 wherein said axis is located inboard from a longitudinal end of said float.
 8. A floating screed device comprising: an elongated float having a planar bottom for floating on plastic concrete, said float having a longitudinal axis; a plurality of rigid rods; a mechanical linkage system coupled to said float and said rods, said linkage system positioning said rods in a spaced-apart parallel fashion and in proximity to one side of said float with tops of said rods defining a planar region aligned with said planar bottom at a neutral position of said floating screed device, said linkage system simultaneously and uniquely adjusting a height of each of said rods relative to said planar bottom of said float as said floating screed device is moved through a volume of the plastic concrete that is unfinished with said rods defining a leading edge between said floating screed device and the volume of the plastic concrete that is unfinished, wherein said planar region rotates about an axis that is parallel to said rods and perpendicular to said longitudinal axis of said float and wherein said planar region forms an angle of inclination with respect to said planar bottom; means coupled to said float for determining elevation thereof relative to a target elevation in the plastic concrete; and a controller coupled to said linkage system and said means for determining elevation, for controlling said linkage system based on said elevation so-determined as said floating screed device is moved through the volume of the plastic concrete that is unfinished.
 9. A floating screed device as in claim 8 wherein said linkage system moves each of said rods along a circular arc with each of said rods being swept through a unique angle.
 10. A floating screed device as in claim 8 wherein said linkage system moves each of said rods along a circular arc with each of said rods being swept through the same angle.
 11. A floating screed device as in claim 8 wherein the length of each of said rods is the same.
 12. A floating screed device as in claim 8 wherein the color of each of said rods is different from that of concrete.
 13. A floating screed device as in claim 8 wherein said axis is one of coincident with said planar bottom and parallel to said planar bottom.
 14. A floating screed device as in claim 8 wherein said axis is located inboard from a longitudinal end of said float.
 15. A floating screed device comprising: an elongated float having a planar bottom for floating on plastic concrete, said float having a longitudinal edge that is beveled from said planar bottom to a height above said planar bottom, said float having a longitudinal axis passing through opposing longitudinal ends of said float; a plurality of rigid rods; a mechanical linkage system coupled to said float and said rods, said linkage system positioning said rods in a spaced-apart parallel fashion with respect to said longitudinal edge of said float with tops of said rods defining a planar region aligned with said planar bottom at a neutral position of said floating screed device, said linkage system simultaneously and uniquely adjusting a height of each of said rods relative to said planar bottom of said float as said floating screed device is moved through a volume of the plastic concrete that is unfinished with said rods defining a leading edge between said floating screed device and the volume of the plastic concrete that is unfinished, wherein said planar region rotates about an axis that is (i) located inboard with respect to one of said longitudinal ends of said float, (ii) parallel to said rode, and (iii) perpendicular to said longitudinal axis of said float, and wherein said planar region forms an angle of inclination with respect to said planar bottom; means coupled to said float for determining elevation thereof relative to a target elevation in the plastic concrete; and a controller, coupled to said linkage system and said means for determining elevation, for controlling said linkage system based on said elevation so-determined as said floating screed device is moved through the volume of the plastic concrete that is unfinished.
 16. A floating screed device as in claim 15 wherein said linkage system moves each of said rods along a circular arc with each of said rode being swept through a unique angle.
 17. A floating screed device as in claim 15 wherein said linkage system moves each of said rods along a circular arc with each of said rods being swept through the same angle.
 18. A floating screed device as in claim 15 wherein the length of each of said rods is the same.
 19. A floating screed device as in claim 15 wherein the color of each of said rods is different from that of concrete.
 20. A floating screed device as in claim 15 wherein said axis is one of coincident with planar bottom and parallel to said planar bottom. 